C# List Conversion In .net?

I have a business object class BusinessObject which implements an interface IAlternateInterface. I already have a method that will return a generic list of BusinessObject which has the objects I want but I want to get them as a list of IAlternateInterface. I tried to do something like the following psudo code but I am getting a "Can not convert source type ... to target type ..." message in Visual Studio. What is the best way to convert the list?

public List<BusinessObject> GetObjects(){
//logic to get the list
}

public List<IAlternateInterface> GetInterfaceObjects(){
return GetObjects();
}